Logical reasoning tasks over symbols, such as learning arithmetic operations and computer program evaluations, have become challenges to deep learning. In particular, even state-of-the-art neural networks fail to achieve \textit{out-of-distribution} (OOD) generalization of symbolic reasoning tasks, whereas humans can easily extend learned symbolic rules. To resolve this difficulty, we propose a neural sequence-to-grid (seq2grid) module, an input preprocessor that automatically segments and aligns an input sequence into a grid. As our module outputs a grid via a novel differentiable mapping, any neural network structure taking a grid input, such as ResNet or TextCNN, can be jointly trained with our module in an end-to-end fashion. Extensive experiments show that neural networks having our module as an input preprocessor achieve OOD generalization on various arithmetic and algorithmic problems including number sequence prediction problems, algebraic word problems, and computer program evaluation problems while other state-of-the-art sequence transduction models cannot. Moreover, we verify that our module enhances TextCNN to solve the bAbI QA tasks without external memory.

提出神经序列到网格（seq2grid）模块，作为输入预处理器，通过自动分段和对齐输入序列到网格的映射，任何以网格输入的神经网络结构，均可以通过端到端训练的方式，搭配我们的模块一起取得新的突破，在包括计算机程序评估在内的各项算数和算法问题上，获得了在样本外泛化能力。

神经序列到网格模块学习符号规则